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<title>Specific Ion interaction Theory (SIT)</title>
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<p>The <b>Specific Ion interaction Theory (SIT)</b> was adopted by the
OECD-NEA thermodynamic database project, and described in its published reviews and books,
see <a href="#Refs">list of references</a>.</p>

<p>In the <b>SIT</b> the <a href="SP_Ionic_Strength.htm#Act_Coef">activity coefficient</a>
of an ion &#147;<i>i</i>&#148; with electric charge <nobr>Z<sub><i>i</i></sub></nobr> is given by:
<table cellspacing="0" cellpadding="0" border="0">
<tr valign="top"><td><tt>&nbsp;&nbsp;&nbsp;</tt></td>
	<td valign="top"><nobr>log <i>&#947;<sub>i</sub></i><font size="+2"> </font>= </nobr></td>
	<td valign="top"><nobr>&#8722;<i>A</i><font size="+2"> </font><i>Z<sub>i</sub></i><sup>2</sup></nobr>
		<nobr><font size="+2">(</font>&#8730;<b><i>I</i></b> &nbsp;/
			<font size="+1">&nbsp;(</font>1+<i>B</i> &#8730;<b><i>I</i></b><font size="-2"> </font>
				<font size="+1">)</font><font size="+2">)</font></nobr>
	<nobr>+ &#8721; <i>&#949;</i>(<i>i</i>,<i>j</i>) <i>m<sub>j</sub></i></nobr>
</td></tr></table></p>

<p class="cont">
where <b><i>I</i></b> is the <a href="SP_Ionic_Strength.htm">ionic strength</a>;
<i>A</i> is the <a href="SP_Ionic_Strength_DH.htm">Debye-H&uuml;ckel</a>
slope (a solvent parameter); <i>B</i> is a temperature-dependent parameter:</p>

<p><center><table cellspacing="0" cellpadding="5" border="1">
<tr><td><nobr><i>t</i> (&deg;C)</nobr></td>
	<td align="center"><i>A</i></td>
	<td align="center"><i>B</i></td></tr>
	<tr><td align="right">0</td><td>&nbsp;0.491</td><td>1.48</td></tr>
	<tr><td align="right">25</td><td>&nbsp;0.509</td><td>1.50</td></tr>
	<tr><td align="right">50</td><td>&nbsp;0.534</td><td>1.52</td></tr>
	<tr><td align="right">100</td><td>&nbsp;0.600</td><td>1.56</td></tr>
  </table></center>
</p>

<p>and <nobr><i>&#949;</i>(<i>i</i>,<i>j</i>)</nobr> is the specific interaction parameters
between the ion &#147;<i>i</i>&#148; and another ion &#147;<i>j</i>&#148; of opposite charge sign.
The summation is taken over all ions <i>j</i> such that <nobr><i>Z<sub>i</sub>&#215;Z<sub>j</sub></i> &gt; 0</nobr>
(opposite electric charge sign). Often the <nobr><i>&#949;</i>-values</nobr> are assumed to be independent of
the ionic strength. A fundamental principle of the <b>SIT</b> is that
<nobr><i>&#949;</i>(<i>i</i>,<i>j</i>)</nobr> = <nobr><i>&#949;</i>(<i>j</i>,<i>i</i>),</nobr>
that is, the specific ion interactions are symmetrical.</p>

<p><nobr><b><i>&#949;</i>-values</b></nobr> in <a href="S_0_Main.htm">SPANA</a> (and
<nobr><a href="SP_0_Main.htm">SED/PREDOM</a>):</nobr></p>

<ul>
<li><p>Default values are first assigned to all ions:</p>
<p style="margin-left:20pt; margin-top:0; margin-bottom:0; text-indent:0;">
<nobr>&#949;(M<sup><i>Z</i>+</sup>,X<sup><i>Y</i>&#8722;</sup>)</nobr>
= 0.15 + <nobr>0.15 (<i>Z</i> + <i>Y</i>).</nobr></p>
<p class="cont">For example:
<nobr>&#949;(K<sup>+</sup>,MoO<sub>4</sub><sup>2&#8722;</sup>)</nobr> = 0, and
<nobr>&#949;(H<sup>+</sup>,OH<sup>&#8722;</sup>)</nobr> = <nobr>0.15.</nobr>
</p></li>

<li><p>For interactions with Na<sup>+</sup>, Cl<sup>&#8722;</sup>
and ClO<sub>4</sub><sup>&#8722;</sup> the
estimation method proposed by <a href="#Refs">Hummel (2009)</a> is used:</p>
<p style="margin-left:20pt; margin-top:0; margin-bottom:0; text-indent:0;">
<nobr>&#949;(Na<sup>+</sup>,X<sup><i>Y</i>&#8722;</sup>)</nobr>
<nobr>= 0.05 <i>Y</i>.</nobr></p>
<p style="margin-left:20pt; margin-top:0; margin-bottom:0; text-indent:0;">
<nobr>&#949;(M<sup><i>Z</i>+</sup>,Cl<sup>&#8722;</sup>)</nobr>
<nobr>= &#8722;0.05 + (0.1 <i>Z</i>).</nobr></p>
<p style="margin-left:20pt; margin-top:0; margin-bottom:0; text-indent:0;">
<nobr>&#949;(M<sup><i>Z</i>+</sup>,ClO<sub>4</sub><sup>&#8722;</sup>)</nobr>
<nobr>= 0.2 <i>Z</i>.</nobr></p>

<p class="cont">For example,
<nobr>&#949;(Sr<sup>2+</sup>,Cl<sup>&#8722;</sup>)</nobr> = <nobr>0.15,</nobr> and
<nobr>&#949;(Na<sup>+</sup>,MoO<sub>4</sub><sup>2&#8722;</sup>)</nobr> = <nobr>&#8722;0.1.</nobr>
</p></li>

<li><p><nobr><i>&#949;</i>-values</nobr>
are finally searched in a file named:</p>
<p class="indent"><nobr>&#147;<tt>SIT-coefficients.dta</tt>&#148;</nobr></p>
<p class="cont">
this file is distributed and stored in the installation folder.
If you wish to add or change <nobr><i>&#949;</i>-coefficients</nobr> you have to
create a copy of the file (with the same name) and store it either in your user directory
(system dependent, shown with the &#147;Help / About&#148; menu), or in the
&#147;working&#148; directory (where your input data file is located). Any
<nobr><i>&#949;</i>-values</nobr> in the &#147;working&#148; directory will
superseede those in the user directory, and the data in the user directory will
superseede those in the installation directory. Any <nobr><i>&#949;</i>-values</nobr>
in these files will superseede the default values.</p></li>
</ul>

<p>The activity of water <nobr>(H<sub>2</sub>O)</nobr> is given by
<table cellspacing="0" cellpadding="0" border="0">
<tr valign="top"><td><tt>&nbsp;&nbsp;&nbsp;</tt></td>
	<td valign="top"><nobr>log <i>a</i><sub>H<sub>2</sub>O</sub><font size="+1"> </font>= </nobr></td>
	<td valign="top"><nobr>&#8722; &Phi; &#8721;<i>m<sub>k</sub></i>&nbsp;/</nobr>
		<nobr><font size="+1">(</font>ln(10)&nbsp;55.508<font size="+1">)</font></nobr>
</td></tr></table></p>

<p class="cont">
where &#147;<i>k</i>&#148; are all solute species in the aqeuous solution, and &#147;&Phi;&#148;
is the osmotic coefficient, calculated using the <b>SIT</b> as follows:
<table cellspacing="0" cellpadding="0" border="0">
<tr valign="top"><td><tt>&nbsp;&nbsp;&nbsp;</tt></td>
	<td valign="top"><nobr>&Phi;<font size="+1"> </font>= </nobr></td>
	<td valign="top">1 &#8722; <nobr>(2/3)</nobr> <nobr><font size="+1">(</font>ln(10)/&#8721;<i>m<sub>k</sub></i><font size="+1">)</font></nobr>
		<nobr><i>A</i>&nbsp;<b><i>I</i></b><sup>3/2</sup></nobr>
		<nobr><i>&sigma;</i>(<i>B</i><font size="-2">&nbsp;</font>&#8730;<b><i>I</i></b>)</nobr>
          <nobr>+&nbsp;<font size="+1">(</font>ln(10)/&#8721;<i>m<sub>k</sub></i><font size="+1">)</font></nobr>
					<nobr>&#8721;<i><sub>i</sub></i> &#8721;<i><sub>j</sub></i>
					<i>&#949;</i>(<i>i</i>,<i>j</i>)&nbsp;<i>m<sub>i</sub></i>&nbsp;<i>m<sub>j</sub></i></nobr>
</td></tr></table></p>
<p class="cont">where &#147;<i>i</i>&#148; are cations or neutral species and &#147;<i>j</i>&#148; are anions,
and
<table cellspacing="0" cellpadding="0" border="0">
<tr valign="top"><td><tt>&nbsp;&nbsp;&nbsp;</tt></td>
	<td valign="top"><nobr>&sigma;</i>(<i>x</i>)<font size="+2"> </font>= </nobr></td>
	<td valign="top"><nobr>(3/<i>x</i><sup>3</sup>)</nobr> <nobr><font size="+2">(</font>(1+<i>x</i>)</nobr> <nobr>&#8722; 1/(1+<i>x</i>)</nobr> <nobr>&#8722; 2 ln(1+<i>x</i>)<font size="+2">)</font></nobr>
</td></tr></table></p>


<a name="Refs"></a>
<h4>References</h4>
<p>
<ul>
<li>
Grenthe, I., Fuger, J., Konings, R.J.M., Lemire, R.J., Muller, A.B.,
Nguyen-Trung, C., <nobr>Wanner, H.</nobr> (1992) <i>Chemical Thermodynamics of Uranium</i>, 715&nbsp;p.
Amsterdam, The Netherlands: North-Holland, Elsevier Sci. Publ. B.V.</li>
<li>
Grenthe, I., Plyasunov, A.V., Spahiu, K. (1997)
Estimations of medium effects on thermodynamic data. In: <i>Modelling In Aquatic Chemistry</i>
<nobr>(I. Grenthe</nobr> &amp; <nobr>I. Puigdomenech,</nobr> eds.), pp. 325-426. Paris, France:
OECD Nuclear Energy Agency (NEA).</li>
<li>
Rand, M.H., Fuger, J., Grenthe, I., Neck, V., <nobr>Rai, D.</nobr> (2008)
<i>Chemical Thermodynamics of Thorium</i>, 900&nbsp;p. Paris, France: OECD Publishing.</li>
<li>
Hummel, W. (2009) Ionic strength corrections and estimation of SIT ion interaction
coefficients, Report <nobr>PSI-TM-44-09-01.</nobr> Paul Scherrer Institut, Switzerland.</li>
</ul>
</p>

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<tt>&nbsp;</tt><a href="SP_Ionic_Strength.htm#Models">Back to activity coefficient models</a></p>

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